Abstract
The “runs” conjecture, proposed by [Kolpakov and Kucherov, 1999], states that the number of occurrences of maximal repetitions (runs) in a string of length n is at most n. The best bound to date, due to [Crochemore and Ilie, 2007], is 1.6n. Here we improve very much this bound using a combination of theory and computer verification. Our best bound is 1.048n but actually solving the conjecture seems to be now only a matter of time.
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Crochemore, M., Ilie, L., Tinta, L. (2008). Towards a Solution to the “Runs” Conjecture. In: Ferragina, P., Landau, G.M. (eds) Combinatorial Pattern Matching. CPM 2008. Lecture Notes in Computer Science, vol 5029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69068-9_27
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DOI: https://doi.org/10.1007/978-3-540-69068-9_27
Publisher Name: Springer, Berlin, Heidelberg
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